Block cipher construction using minimum spanning tree from graph theory and its application with image encryption.

Area of Science:

• Cryptography and Information Security
• Applied Mathematics and Graph Theory

Background:

• Substitution Boxes (S-boxes) are fundamental components in modern cryptography for enhancing encryption security by introducing confusion.
• Increasingly sophisticated cyber threats necessitate the development of more robust and dynamic S-box designs.
• Existing S-box construction methods may not fully address the evolving landscape of cryptographic attacks.

Purpose of the Study:

• To propose and evaluate a novel method for constructing cryptographically secure S-boxes.
• To leverage graph theory, specifically Minimum Spanning Trees (MST) of cycle graphs, for S-box generation.
• To assess the performance and security of the proposed S-box against existing designs and in image encryption.

Main Methods:

• Constructing cycle graphs from plaintext, assigning ASCII values to vertices, and calculating inter-vertex distances.
• Generating a Minimum Spanning Tree (MST) graph from the cycle graph.
• Deriving the S-box from the adjacency matrix of the MST graph, enhanced with S₂₅₆ permutation for increased unpredictability.

Main Results:

• The proposed graph-theory-based S-box construction method yields cryptographically secure S-boxes.
• Performance evaluations and cryptographic tests show the proposed S-box is robust and outperforms existing designs.
• Application in an image encryption scheme demonstrates the S-box's efficacy and suitability for practical security solutions.

Conclusions:

• The novel method effectively generates strong and unpredictable S-boxes using graph theory principles.
• The proposed S-boxes offer significant improvements in cryptographic security, particularly against advanced hacking techniques.
• This approach provides a valuable contribution to the field of cryptography, enhancing data and image security.